# Worksheet on H.C.F. of Monomials

Practice the worksheet on H.C.F. of monomials. The questions are based on finding the highest common factor of two or more monomials.

We know, the highest common factor (H.C.F.) of two or more monomials is the monomial of highest dimensions which divides each of them without remainder.

For example: The highest common factor of m6, m5, m4, m3, m2 is m2.

If the monomials have numerical coefficients, find by Arithmetic their greatest common measure, and prefix it as a coefficient to the algebraical highest common factor.

For example: The highest common factor of 14m4a3b, 21m2a4b and 35m3ab4 is 7m2ab; for it consists of the product of:

(i) the greatest common measure of the numerical coefficients;

(ii) the highest power of each letter which divides everyone of the given expressions.

1. Find the highest common factor (H.C.F.) of the two monomials:

(i) a2b and a2b2

(ii) a2b2c3 and a2b2c2

(iii) 15x2y3 and 6x3y2

(iv) 4a2 and 10ab

(v) 21x2y and 49xy2

(vi) a3b2 and – 5b2

(vii) 26a3y2k4 and 39a2y4k2

(viii)24m2n3 and 32m3n4

(ix) 81x2y4z2 and 18x3y3z

(x) 18x3y2z4 and 54x2y4z

(xi) 20a2b3c4 and 70a3b2z2

(xii) 16x2y3 and 60x3y2

2. Find the highest common factor (H.C.F.) of the three monomials:

(i) 3x2y2, 6x3y and 4x4y2

(ii) 13x2y3, 17x2y2m and 7m2z

(iii) 8a2m, 6abmn and 10abm3n2

(iv) 49ma2, 63mb2 and 56mc2

(v) 17xy2z, 34x2yz and 51xyz2

(vi) 25ab2c, 100a2bc and 125ab

(vii) 4a3, 6b2 and 8c

(viii) 2m2n3, 10m3n2, 14mn

(ix) 5z3, - 15z2 and 45z

(x) 42p2q2r, 63p3q and 56p2r

(xi) 15x5y3z7, 60x3y7z6 and 25x4y5z2

(xii) 35p2qr3, 42p3q2r and 30pq2r3

Answers for the worksheet on H.C.F. of monomials are given below to check the exact answers of the above questions.

1. (i) a2b

(ii) a2b2c2

(iii) 3x2y2

(iv) 2a

(v) 7xy

(vi) b2

(vii) 13a2y2k2

(viii) 8m2n3

(ix) 9x2y3z

(x) 18x2y2z

(xi) 10a2b2z2

(xii) 4x2y2

2. (i) x2y

(ii) 1

(iii) 2am

(iv) 7m

(v) 17xyz

(vi) 25ab

(vii) 2

(viii) 2mn

(ix) 5z

(x) 7p2

(xi) 5x3y3z2

(xii) pqr